CHAIN RULE
This module will teach you the basics of direct and indirect proportions. These concepts will further help you in time and work questions.
Important Formulas – chain rule
- Direct Proportion
Two quantities are said to be directly proportional, if on the increase or decrease of the one, the other increases or decreases the same extent.
Examples
- Indirect Proportion (inverse proportion)
Two quantities are said to be indirectly proportional (inversely proportional) if on the increase of the one, the other decreases to the same extent and vice-versa.
Examples
- Number of days needed to complete a work is indirectly proportional (inversely proportional) with the number of persons who does the work (More Persons, Less Days needed)
- The time taken to travel a distance is indirectly proportional (inversely proportional) with the speed in which one is travelling (More Speed, Less Time)
Solved Examples
Level 1
1. If the cost of x metres of wire is d rupees, then what is the cost of y metres of wire at the same rate? | |
A. Rs. (xd/y) | B. Rs. x/d |
C. Rs. (yd/x) | D. Rs. y/d |
Answer : Option C
Explanation :
cost of x metres of wire = Rs. d
cost of 1 metre of wire = Rs.(d/x)
cost of y metre of wire = Rs.(y×d/x)=Rs. (yd/x)
2. In a camp, there is a meal for 120 men or 200 children. If 150 children have taken the meal, how many men will be catered to with remaining meal? | |
A. 50 | B. 30 |
C. 40 | D. 10 |
Answer : Option B
Explanation :
Meal for 200 children = Meal for 120 men
Meal for 1 child = Meal for 120/200 men
Meal for 150 children = Meal for (120×150)/200 men=Meal for 90 men
Total mean available = Meal for 120 men
Renaming meal = Meal for 120 men – Meal for 90 men = Meal for 30 men
3. 36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work? | |
A. 26 | B. 22 |
C. 12 | D. 24 |
Answer : Option D
Explanation :
Let the required number of days be x
More men, less days (indirect proportion)
Hence we can write as
Men36:27}::x:18 ⇒36×18=27×x ⇒12×18=9×x
⇒12×2=x
⇒x=24
| |
A. 15 | B. 12 |
C. 21 | D. 9 |
Answer : Option D
Explanation :
Let the number of revolutions made by the larger wheel be x
More cogs, less revolutions (Indirect proportion)
Hence we can write as
Cogs 6:14}: x: 21 ⇒6×21=14×x ⇒6×3=2×x ⇒3×3=x ⇒x=9
5. 3 pumps, working 8 hours a day, can empty a tank in 2 days. How many hours a day should 4 pumps work in order to empty the tank in 1 day? | |
A. 10 | B. 12 |
C. 8 | D. 15 |
Answer : Option B
Explanation :
Let the required hours needed be x
More pumps, less hours (Indirect proportion)
More Days, less hours (Indirect proportion)
Hence we can write as
Pumps 3:4
::x:8
Days 2:1
⇒3×2×8=4×1×x
⇒3×2×2=x
⇒x=12
6. 39 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work? | |
A. 9 | B. 12 |
C. 10 | D. 13 |
Answer : Option D
Explanation :
Let the required number of days be x
More persons, less days (indirect proportion)
More hours, less days (indirect proportion)
Hence we can write as
Persons 39:30
::x:12
Hours 5:6
⇒39×5×12=30×6×x ⇒39×5×2=30×x ⇒39=3×x ⇒x=13
7. A certain industrial loom weaves 0.128 meters of cloth every second. Approximately how many seconds will it take for the loom to weave 25 meters of cloth? | |
A. 205 | B. 200 |
C. 180 | D. 195 |
Answer : Option D
Explanation :
Let the required number of seconds be x
More cloth, More time, (direct proportion)
Hence we can write as
Cloth 0.128:25} :: 1:x
⇒0.128x=25 ⇒x=25/0.128 ⇒25000/128=3125/16≈195
8. 21 goats eat as much as 15 cows. How many goats each as much as 35 cows? | |
A. 49 | B. 32 |
C. 36 | D. 41 |
Answer : Option A
Explanation :
15 cows ≡ 21 goats
1 cow ≡21/15 goats
35 cows ≡ (21×35)/15 goats≡(21×7)/3 goats≡7×7 goats ≡ 49 goats
Level 2
1. In a dairy farm, 40 cows eat 40 bags of husk in 40 days. In how many days one cow will eat one bag of husk? | |
A. 1 | B. 40 |
C. 20 | D. 26 |
Answer : Option B
Explanation :
Assume that in x days, one cow will eat one bag of husk.
More cows, less days (Indirect proportion)
More bags, more days (direct proportion)
Hence we can write as
Cows 40:1 ::x:40
Bags 1:40
⇒40×1×40=1×40×x ⇒x=40
2. If a quarter kg of potato costs 60 paise, how many paise does 200 gm cost? | |
A. 65 paise | B. 70 paise |
C. 52 paise | D. 48 paise |
Answer : Option D
Explanation :
Let 200 gm potato costs x paise
Cost of ¼ Kg potato = 60 Paise
=> Cost of 250 gm potato = 60 Paise (∵ 1 Kg = 1000 gm => ¼ Kg = 1000/4 gm = 250 gm)
More quantity, More Paise (direct proportion)
Hence we can write as
Quantity 200:250} :: x:60
⇒200×60=250×x ⇒4×60=5×x ⇒4×12=x ⇒x=48
3. A contract is to be completed in 56 days if 104 persons work, each working at 8 hours a day. After 30 days, 2/5 of the work is completed. How many additional persons should be deployed so that the work will be completed in the scheduled time, each person’s now working 9 hours a day. | |
A. 160 | B. 150 |
C. 24 | D. 56 |
Answer : Option D
Explanation :
Persons worked = 104
Number of hours each person worked per day = 8
Number of days they worked = 30
Work completed = 2/5
Remaining days = 56 – 30 = 26
Remaining Work to be completed = 1 – 2/5 = 3/5
Let the total number of persons who do the remaining work = x
Number of hours each person needs to be work per day = 9
More days, less persons(indirect proportion) More hours, less persons(indirect proportion)
More work, more persons(direct proportion)
Hence we can write as
Days 30:26
Hours 8:9 ::x:104
Work 35:25
⇒30×8×3/5×104=26×9×2/5×x
⇒x=(30×8×3/5×104)/(26×9×2/5)=(30×8×3×104)/(26×9×2)
=(30×8×104)/(26×3×2)=(30×8×4)/(3×2)=5×8×4=160